suddenly vs of a sudden

suddenly and of a sudden both are adverbs.

Word	Noun	Adjective	Verb	Adverb
suddenly	No	No	No	Yes
of a sudden	No	No	No	Yes

As adverbs, suddenly and of a sudden are synonyms defined as:

Other synonyms of suddenly include abruptly, all of a sudden, dead, on the spur of the moment, short.

suddenly (adverb)	of a sudden (adverb)
quickly and without warning; happening unexpectedly; on impulse; without premeditation	quickly and without warning; happening unexpectedly; on impulse; without premeditation